Science, Marxism and the Big Bang: A Critical
Review of 'Reason in
Revolt'

Hegel on the dialectics of infinity

Throughout his life, the German
philosopher Hegel was an enthusiastic supporter of the French Revolution
of 1789. Widely thought of as the most difficult of all
philosophers to understand, Hegel followed in the radical philosophical
tradition begun by Kant, who established a school of philosophy called
German Idealism. Yet Hegel’s idealist philosophy, and in particular
his dialectics, when placed on a materialist basis by Karl Marx and
Friedrich Engels, became one of the cornerstones of Marxism. In their
youth, both Marx and
Engels were 'Young Hegelians', radical opponents of the old
autocracy of the German nation.

Engels comments that, "the true significance and the revolutionary
character of the Hegelian philosophy [was] that it once for all dealt the
death blow to the finality of all products of human thought and action."
He continues:

Truth lay now in the process of cognition itself, in the long
historical development of science, which mounts from lower to ever
higher levels of knowledge without ever reaching, by discovering
so-called absolute truth, a point at which it can proceed no further,
where it would have nothing more to do than to fold its hands and gaze
with wonder at the absolute truth to which it had attained. (Feuerbach
and the End of Classical German Philosophy, in Marx and EngelsSelected Works, p588)

This alone should give Woods pause before
asserting, as a statement of
absolute truth, that "Dialectical materialism conceives of the universe as
infinite", folding his hands, and gazing with wonder at the
discoveries he has made.

There are more than a few respects in which, as Engels comments, the
materialist outlook penetrated into Hegel’s philosophy. "Hegel laboured to
discover and demonstrate the pervading thread of development" in the
wide range of fields he studied, and in
doing so, "he played an epoch making role in every sphere". The forced
constructions of Hegel’s "system" are only the frame and scaffolding of
his work, Engels says:

If one does not loiter here needlessly, but presses on farther into
the immense building, one finds innumerable treasures which today
still possess undiminished value. (Feuerbach and the End of
Classical German Philosophy, Selected Works, p590)

Hegel on Aristotle's ‘potential’ and ‘actual’
infinity

Hegel explicitly defends Aristotle’s point of view on the infinite
-
that there is no "actual" infinity, only a potential infinity. Hegel says
that: "The solutions propounded by Aristotle of these dialectical forms
merit high praise". Hegel criticises the seventeenth century French
philosopher, Pierre Bayle, who, Hegel says, argued that "if matter is infinitely
divisible, then it actually contains an infinite number of parts…
[it is] an infinite that really and actually exists." (Science of Logic, pp198-9, § 427. NB The paragraph marks
('§') are useful if the reader wants to reference the internet version of
Science of Logic on the Marxists Internet Archive
www.marxists.org, at
http://www.marxists.org/reference/ archive/hegel/works/hl/index.htm)

"On the contrary", Hegel continues, this is only a "possibility, not an
existing of the parts" (here Hegel substitutes the word
"possibility" where Aristotle would use the word "potential").

Hegel says that Bayle commits the "error of holding mental fictions,
such abstractions, as an infinite number of parts, to be something true
and actual". (Science of Logic, p199, § 427)

Hegel and Newton’s calculus

It appears that Woods is unfamiliar with what Hegel had to say on the
infinite, although there are some seventy references to Hegel throughout
Reason in Revolt. Hegel in general takes a position closer to
materialism than Woods on this question; Woods is more idealist.

Hegel illuminates his views on the infinite by considering the
following stanza of poetry by the eighteenth century German scientist and
poet Albrecht von Haller.

I heap up monstrous numbers,

Pile millions upon millions,

I put aeon upon aeon and world upon world,

And when from that awful height

Reeling, again I seek thee,

All the might of number increased a thousandfold

Is still not a fragment of thee.

I remove them and thou liest wholly before me.

(Quoted in Science of Logic, p230, § 507)

Hegel remarks:

When this heaping and piling up of numbers is regarded as what is
valuable in a description of eternity, it is overlooked that the poet
himself declares this so-called terrifying journey into the beyond to
be futile and empty.

Hegel argues in various passages that it is futile and false to
conceive of an infinite which exists somewhere "beyond". In fact,
in his Science of Logic, Hegel
appears to entirely reject the notion that the universe extends infinitely. Woods
strives to make a complete distinction between the finite and the
infinite, describing the infinite as, at first sight, "beyond all human
experience", but Hegel rejects that separation.

Woods says:

The idea of the infinite seems difficult to grasp, because, at
first sight, it is beyond all human experience… Mathematics deals with
definite magnitudes. Infinity by its very nature cannot be counted or
measured. This means there is a real conflict between the two. (Reason
in Revolt, p353)

But Hegel says:

Thus the infinite does not stand as something finished and complete
above or superior to the finite, as if the finite had an enduring
being apart from or subordinate to the infinite. (Science
of Logic,p138, § 274)

Yet Woods represents Hegel’s outlook in the following way:

In the section on Quantity in the first volume of The Science of
Logic, Hegel points out that, while the introduction of the
mathematical infinite opened up new horizons for mathematics, and led
to important results, it remained unexplained, because it clashed with
the existing tradition and methods. (Reason in Revolt, p355)

This is misleading. Firstly, one should start with the section
Infinity, in the Science of Logic, if one wants to know Hegel’s
thoughts on the infinite directly. But Hegel is no less forthright in the
section on Quantity to which Woods refers – the stanza of poetry
above is from this section. Here Hegel examines Kant’s antinomy as to
whether the world is finite or infinite. Woods mentions this antinomy, and
comments "It fell to the great dialectician Hegel to resolve the
contradiction in The Science of Logic." (Reason in Revolt, p
146) So he did. But Woods fails to mention how Hegel resolves it. Hegel
concludes his discussion with following reference to the dialectics of
ancient Greece:

But the so-called world… is never and nowhere without
contradiction, but it is unable to endure it and is, therefore,
subject to coming-to-be and ceasing-to-be. (Science of Logic,
p238, § 529)

Hegel, in other words, does not embrace a universe which is infinite in
time and space in the Newtonian sense, but instead argues that the
universe has a birth and a death.

Nevertheless, it is true, as Woods
infers, that in a remark on The Specific Nature of the Notion of the
Mathematical Infinite, Hegel begins by recognising that the
mathematical infinite led to "important results". (Science of Logic,
p240, § 538) But let us be clear. Hegel here calls the infinities which
mathematics uses, whether infinitely large or infinitely small, "pictorial
conceptions which, when looked at more closely, turn out to be nebulous
shadowy nullities", in other words, which turn out not to exist. (Science
of Logic, p238, § 530)

In calculus (which Hegel is discussing here), a series of numbers gets
smaller, appearing to be an infinite series. But this series never reaches
infinity. Instead, a new quality emerges from the result of the
calculus. (Science of Logic, pp244-5 § 548ff) Hegel sees the dialectic at
work here, where a new quality emerges from a quantitative process. For
this reason, among others, Hegel praises the Newtonian method of calculus.
(Science of Logic, p257, § 580) Hegel is normally in the habit of
sharply criticising Newton in the Science of Logic.

Hegelian infinity: the negation of the negation

In his section Infinity, Hegel discusses the dialectic of a
simple infinite series (a series where, for instance, you can always add
one more to whatever number you arrive at). Each step in the series
appears to be a step towards infinity, Hegel says, only to be negated,
because this step takes you no nearer infinity at all. There is no point
at which infinity is nearer, no matter how many numbers one counts, as the
stanza of poetry which Hegel quotes demonstrates. Thus infinity can be
said to be ‘negated’ by the finite.

But, yet, the counting has not stopped, and there is no conceivable
point at which it will stop. So the finite is once again negated. In this
way, Hegel introduces his famous "negation of the negation", because this
second negation can be called the negation of the first negation, or the
"negation of the negation". Once familiar, this concept is not complex.
The finite is negated by the infinite, and then this negation of infinity
is itself negated with the next finite step in the infinite series, which
again raises the hope of achieving infinity. "The infinite is the negation
of the negation", Hegel states. (Science of Logic,p137, §
273)

The infinite, concludes Hegel, always contains the finite within it,
and is comprised of the finite:

The finite reappears in the infinite itself as its other, because
it is only in its connection with its other, the finite, that the
infinite is. (Science of Logic,p142, § 285)

The infinite, Hegel says, again referring back to ancient Greece, is
properly understood "essentially only as a becoming" (Science of
Logic, p148, § 301), something that is in a process of further
determination. Hegel’s dialectic is a way of explaining why we consider,
or can call, an infinite series ‘infinite’, although it never reaches
infinity. Hegel emphasises that there is no "progress"towards
infinity, since it is always negated and never gets nearer; there is only
an infinite "process" which never leaves the finite.

Woods asks: "How can the universe be finite, and yet have no
boundaries?" (Reason in Revolt, p218) Hegel supplies the essence of
the answer to this question, precisely one century before Einstein’s
general theory of relativity allowed that the curvature of space-time
might cause the universe to curl round on itself: "the image of true
infinity, bent back onto itself, becomes the circle." (Science
of Logic,p149, § 302) To put it another way, the surface of
any sphere is finite yet has no boundaries – an ant can crawl over a
football forever, never coming to an end point, a boundary marking the end
of the sphere.

Hegel and "bad infinity"

Woods says:

In mathematics, it is possible to have an infinite series of
numbers which starts with one. But, in practice, the idea of infinity
cannot begin with one, or any other number. Infinity is not a
mathematical concept. It cannot be counted. This one-sided "infinity"
is what Hegel calls bad infinity. (Reason in Revolt,
p218)

Hegel disparaged those who considered the infinite as something
separate from the finite. The term "bad" infinity, used here by Woods, has been
replaced by the term "spurious" infinity in the modern translation of
Hegel’s Science of Logic. The Moscow (Progress Press, Lawrence and
Wishart) translations of Engels’ Anti-Dühring use the term "bad"
infinity, but the highly regarded 1969 translation of Hegel’s Science
of Logic by A.V. Miller (a translation which marked the beginning of a
revival of interest in Hegel) translates term to which Engels was
referring as "spurious" rather than "bad".

It should be apparent from the foregoing discussion that Woods has
misunderstood what Hegel believed. Hegel did not accept the actual
existence of an infinity which exists apart from processes which can
indeed be counted, whether mathematical or historical, except in his
somewhat pantheistic concept of divinity.

While Woods argues that the finite and the infinite are qualitatively
distinct, Hegel says:

The infinite as thus posited over against the finite, in a relation
wherein they are as qualitatively distinct others, is to be called the
spurious infinite.(Science of Logic,
p139, § 277)

Hegel’s spurious or bad infinity is the complete opposite of Woods’
description of it, and it is precisely Hegel’s spurious or bad infinity
which Woods embraces – the infinity which cannot be counted, which stands
apart from the finite, an infinite which "really and actually exists" as
Bayle had said. Hegel says that: "such an infinite must be seen as a
falsity". (Science of Logic,p149, § 302)

Hegel correctly associates this spurious infinity with the divine. When
Woods repeats a favourite phrase of Ted Grant’s, that the infinite universe
contains "only galaxies and more galaxies stretching out to
infinity", that is Hegel’s bad infinity. Grant and Woods completely
reverse the position that Hegel takes, and which Engels correctly
champions.

Commenting on the Hubble telescope, the telescope which was launched
into space and has captured many stunning images, Woods says:

For our part, we welcome these epoch-making investigations, because
they take the debate about the Big Bang out of the realm of abstract
theorising and mathematical models, and into the field of practical
observation.

We will predict now that they will see new surprises: not the Big
Bang, but only galaxies and more galaxies stretching out to infinity.
(Reason in Revolt, Preface to the 2001 Spanish edition,
emphasis in original)

The Big Bang had long been taken out of abstract theorising, while on
the other hand, infinity will not be seen through the Hubble telescope.
When astronomers turn their telescopes to view galaxies whose light has
travelled to us over millions and billions of years, they are looking back
in time in the sense that what they see actually took place millions or
even billions of years ago, but its light has only just reached us. And
what they see when they look back in time, in general, are galaxies in an
earlier stage of formation and development. They see, for instance,
galaxies in which the stars have not had time to manufacture as many of
the elements that over millions and billions of years are products of the
fusion process that powers the stars.

Woods omits to acknowledge that this is the overall picture. This
process of the development of galaxies from the remnants of the Big Bang
will be glanced at later. But what is not seen through telescopes is a
mixture of older and younger galaxies irrespective of distance. There are
no objects which challenge the widest range of ages given the universe,
from ten to twenty billons years. The concept of an infinite universe
containing "galaxies and more galaxies stretching out to infinity"
is in conflict with the evidence, and has been for a very long time.

But only a year after his comments on the Hubble telescope in 2001,
writing in the preface to the 2002 USA edition of Reason in Revolt,Woods endorsed a version of the 70-year-old cyclical Big Bang theory
that interprets space as finite but time as infinite. Presumably, Woods
was therefore prepared to accept the fallacy of the confident prediction
of the previous year, of "only galaxies and more galaxies
stretching out to infinity", a prediction which, after all, is not and
cannot be based on practical observation at all, only on abstract
theorising. However far one can see, one can never see infinity through a
telescope.

The idealist philosopher Hegel supports the materialist view that
infinity is an abstraction that is never realised, except, that is, in god
– Hegel is still an idealist. Woods takes the idealist position, which
Hegel calls "spurious" or "bad" infinity. It is an undialectical position,
Hegel says:

The falsification of the finite and infinite by the understanding
which holds fast to a qualitatively distinct relation between them and
asserts that each in its own nature is separate from the other, comes
from forgetting what the Notion [dialectic] of these movements is. (Science
of Logic,p145, § 293)

Hegel has firmer dialectical reasons for rejecting the concept of a
progression towards infinity. It is not just that infinity could never be
reached or brought any nearer. For Hegel no apparently infinite process
will go on indefinitely. Hegel understood that each additional quantity
added to an infinite series could – and at some point in the concrete,
material world, will– lead to a qualitative leap, and the whole
process will be transformed into something else. Nothing stays the same.
Everything comes into being and passes away. In the same way, those
processes that we imagine could continue forever are mere figments of our
imagination. When infinities appear in equations, physicists invariably
work on the assumption that these infinities only mark out a point of
qualitative transformation, or phase change. The idea of infinite space,
stretching on without limit is undialectical because it is an idea of
quantitative accumulation without a qualitative change.

Hegel explains that bad or spurious infinity "… is
commonly held to be something sublime and a kind of divine worship". (Science
of Logic,p228, § 504) He clearly considers Woods' approach
undialectical:

A second question in these metaphysical systems was: Is the world
finite or infinite? The very terms of the question assume that the
finite is a permanent contradictory [i.e. in permanent contradiction]
to the infinite…

Dogmatism consists in the tenacity which draws a hard and fast line
between certain terms and others opposite to them. We may see this
clearly in the strict ‘either – or’: for instance, The world is either
finite or infinite; but one of these two it must be. The contrary of
this rigidity is the characteristic of all [dialectical] truth.
(Hegel, Encyclopaedia,paragraph 28 (remark), paragraph
32)

We must, however, add a caveat. Engels explains that the Hegelian
system presented itself in such a way that, in the final pages of his
Science of Logic: "the whole dogmatic content of the Hegelian system
is declared to be absolute truth, in contradiction to his dialectical
method, which dissolves all dogmatism". (Feuerbach and the End of
Classical German Philosophy, in Marx and EngelsSelected
Works, p589)

Hegel incorporated Kant’s support for Newtonian absolute space (not to
be confused with infinite space) into his philosophy. In the closing pages
of Science of Logic, Hegel appears to mystically link absolute
space and time with what he terms the Absolute Idea, a kind of
mystical godhead.

Hegel writes that the Absolute Idea takes on the form of the "externality
of space and time existing absolutely on its own account without the
moment of subjectivity". (Science of Logic, p843, § 1817) In a
sense, Hegel is suggesting that once the Absolute Idea is reached in a
great mystical cycle of the dialectical development of all things towards
godhead, it returns, albeit at a higher level, to "nature", "the end being
wound back into the beginning, the simple ground", (Science of Logic,
pp842-3, § 1814)

But this does not mean that Hegel endorses Newton’s concept of an
infinite universe. Space and time are absolute, in his view, but not
infinite. Even in the closing paragraphs of Science of Logic, which
contain an exposition of his dialectic – so that one might easily suppose
that the "Absolute Idea" is nothing other than Hegel’s dialectic – Hegel
argues that the infinite is not in fixed opposition to the finite, as
something "beyond".